As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following equations best represents the graph shown in Image 1 (a parabola opening upward with vertex below the x-axis)?

Accepted Answer

$$f(x) = x^2$ + 6x + 5$$

Question 2

For the graph shown in Image 2 (a parabola opening downward), what is the nature of its vertex?

Accepted Answer

The vertex is a maximum.

Question 3

Which function corresponds to the graph in Image 3 (a straight line with positive slope)?

Accepted Answer

$$f(x) = x$$

Question 4

Given the graph in Image 4 (a parabola opening upward with vertex at the origin), which of the following is the correct equation?

Accepted Answer

$$f(x) = x^2$

Question 5

The graph in Image 5 shows a cubic function. Which property is true about its end behavior?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 6

Which of the following best describes the graph in Image 6 (a parabola opening upward, narrower than $$y = x^2$)?

Accepted Answer

$$f(x) = 2x^2$

Question 7

If a quadratic function has its vertex at $$(h, k)$$ and opens upward, which form represents this function?

Accepted Answer

$$f(x) = a(x-h)^2$ + k$$, where $$a \u003e 0$$

Question 8

Which of the following statements about the graph in Image 1 is correct?

Accepted Answer

The axis of symmetry is $$x = -3$$

Question 9

For the function $$f(x) = -x^2$ - 4x - 3$$, which graph best represents its shape?

Accepted Answer

Image 2

Question 10

Which graph represents a function with a minimum value at its vertex?

Accepted Answer

Image 1

Quadratic and Polynomial Functions: Definitions, Properties, and Theorems

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